Andy Clark and David Chalmers claim that cognitive processes can and do extend outside the head.1 Call this the “hypothesis of extended cognition” (HEC). HEC has been strongly criticised by Fred Adams, Ken Aizawa and Robert Rupert.2 In this paper I argue for two claims. First, HEC is a harder target than Rupert, Adams and Aizawa have supposed. A widely-held view about the nature of the mind, functionalism—a view to which Rupert, Adams and Aizawa appear to subscribe— entails HEC. Either HEC is true, or functionalism is false. The relationship between functionalism and HEC goes beyond support for the relatively uncontroversial claim that it is logically or nomologically possible for cognition to extend (the “can” part of HEC); functionalism entails that cognitive processes do extend in the actual world. Second, I argue that the version of HEC entailed by functionalism is more radical than the version that Clark and Chalmers suggest. I argue that it is so radical as to form a counterexample to functionalism. If functionalism is modified to prevent these consequences, then HEC falls victim to Rupert, Adams and Aizawa’s original criticism. An advocate of HEC has two choices: (1) accept functionalism and radical HEC; (2) give up HEC entirely. Clark and Chalmers’ intermediate position of a modest form of HEC is unsustainable. The argument of this paper, although initially appearing to support Clark and Chalmers, ultimately argues against their position. The price of HEC is rampant expansion of the mind into the world, and the implausibility of such expansion is indicative of deep-seated problems with functionalism. The argument of this paper consequently speaks to wider issues than just the status of HEC. The reasons for..